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Updated: Feb 2, 2026

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
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An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method.

Wen Zhang1, Hui Zhang2, Shijiu Jin3

  • 1State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China. baswen@tju.edu.cn.

Micromachines
|November 9, 2018
PubMed
Summary

A new analytical model accurately predicts Capacitive Micromachined Ultrasonic Transducer (CMUT) multilayer membrane performance. This model enhances CMUT design by providing precise static deflection and response frequency predictions.

Keywords:
capacitive micromachined ultrasonic transducer (CMUT)frequency responsemultilayer membraneresidual stress compensationstatic deflection

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Area of Science:

  • MEMS/NEMS
  • Ultrasonic Transducers
  • Materials Science

Background:

  • Capacitive Micromachined Ultrasonic Transducer (CMUT) multilayer membranes are critical for performance.
  • Existing analytical models often oversimplify multilayer membranes, leading to inaccuracies.
  • Accurate modeling of multilayer membranes is essential for CMUT design and optimization.

Purpose of the Study:

  • To develop a novel analytical model for CMUTs with multilayer membranes.
  • To accurately predict static deflection and response frequency under external pressures.
  • To provide a reliable tool for CMUT design and optimization.

Main Methods:

  • Utilized the Ritz method and Hamilton's principle for model derivation.
  • Established mathematical relationships between external pressure, static deflection, and response frequency.
  • Incorporated a residual stress compensation method.

Main Results:

  • The model accurately predicts static deflection and response frequency for three-layer and double-layer CMUT membranes.
  • Relative errors for static deflection ranged from 0.71% to 3.51%.
  • Relative errors for response frequencies were between 0.35% and 4.96%, with a 4.14% error for central deflection in double-layer membranes.

Conclusions:

  • The proposed analytical model offers rapid and accurate predictions for multilayer CMUT membranes.
  • The model demonstrates significant improvement over simplified monolayer models.
  • It serves as a valuable reference for CMUT design and optimization.